Frequently Asked Questions in Quantitative Finance, Second Edition

625 Pages·2009·3.81 MB·English

by  Paul P. Wilmott

Frequently Asked Questions
In
Quantitative Finance
... includingkeymodels,importantformulæ,
popularcontracts,essaysandopinions,ahistory
ofquantitativefinance,sundrylists,the
commonestmistakesinquantfinance,
brainteasers,plentyofstraight-talking,the
Modellers’Manifestoandlotsmore
www.wilmott.com
Paul Wilmott
A John Wiley and Sons, Ltd., Publication

Frequently Asked Questions
In
Quantitative Finance
... includingkeymodels,importantformulæ,
popularcontracts,essaysandopinions,ahistory
ofquantitativefinance,sundrylists,the
commonestmistakesinquantfinance,
brainteasers,plentyofstraight-talking,the
Modellers’Manifestoandlotsmore
www.wilmott.com
Paul Wilmott
A John Wiley and Sons, Ltd., Publication
This edition first published 2009
 2009 Paul Wilmott
Registered Office
John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, P019 8SQ, United
Kingdom
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Library of Congress Cataloging-in-Publication Data
Wilmott, Paul.
Frequently asked questions in quantitative finance / by Paul Wilmott. — 2nd ed.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-470-74875-6
1. Finance—Mathematical models. 2. Investments—Mathematical models. 3.
Options (Finance)—Mathematical models. I. Title.
HG4515.2.W55 2009
(cid:1)
332.6015118—dc22
2009027978
A catalogue record for this book is available from the British Library.
ISBN 978-0-470-74875-6
Typeset in 9/10.5 Cheltenham-Book by Laserwords Private Limited, Chennai, India
Printed in Italy by Printer Trento
Tomyparents
Paul Wilmott has been called ‘the smartest of the quants, he
may be the only smart quant’ (Portfolio magazine/Nassim
Nicholas Taleb), ‘cult derivatives lecturer’ (Financial Times),
‘expert on quantitative easing,’ (Guardian)∗, ‘the finance
industry’s Mozart’ (Sunday Business) and ‘financial
mathematics guru’ (BBC).
∗This was, of course, a typical Grauniad mistake.
Contents
Preface to the Second Edition x
Preface to the First Edition xiii
1 The Quantitative Finance Timeline 1
2 FAQs 21
3 The Financial Modellers’ Manifesto 253
4 Essays 259
5 The Commonest Mistakes in Quantitative Finance:
A Dozen Basic Lessons in Commonsense for Quants
and Risk Managers and the Traders Who Rely
on Them 313
6 The Most Popular Probability Distributions
and Their Uses in Finance 383
7 Twelve Different Ways to Derive Black–Scholes 401
8 Models and Equations 429
9 The Black–Scholes Formulæ and the Greeks 453
10 Common Contracts 459
11 Popular Quant Books 483
12 The Most Popular Search Words and Phrases
on Wilmott.com 497
13 Brainteasers 507
14 Paul & Dominic’s Guide to Getting a Quant Job 557
Index 579
Frequently Asked
Questions
1. What are the different types of mathematics found
in quantitative finance? 22
2. What is arbitrage? 27
3. What is put–call parity? 30
4. What is the Central Limit Theorem and what are its
Implications for finance? 33
5. How is risk defined in mathematical terms? 38
6. What is value at risk and how is it used? 42
7. What is Extreme Value Theory? 46
8. What is CrashMetrics? 48
9. What is a coherent risk measure and what are
its properties? 52
10. What is Modern Portfolio Theory? 55
11. What is the Capital Asset Pricing Model? 58
12. What is Arbitrage Pricing Theory? 62
13. What is Maximum Likelihood Estimation? 65
14. What is cointegration? 71
15. What is the Kelly criterion? 74
16. Why hedge? 77
17. What is marking to market and how does it affect
risk management in derivatives trading? 83
vii
Frequently Asked Questions
18. What is the Efficient Markets Hypothesis? 87
19. What are the most useful performance measures? 90
20. What is a utility function and how is it used? 93
21. What is the difference between a quant and an
actuary? 97
22. What is a Wiener process/Brownian motion and
what are its uses in finance? 100
23. What is Jensen’s Inequality and what is its role
in finance? 103
24. What is Itoˆ’s lemma? 106
25. Why does risk-neutral valuation work? 109
26. What is Girsanov’s theorem, and why is it
important in finance? 113
27. What are the greeks? 116
28. Why do quants like closed-form solutions? 122
29. What are the forward and backward equations? 125
30. What is the Black–Scholes equation? 129
31. Which numerical method should I use and when? 132
32. What is Monte Carlo simulation? 141
33. What is the finite-difference method? 145
34. What is a Poisson process and what are its uses
in finance? 150
35. What is a jump-diffusion model and how does
it affect option values? 152
36. What is meant by ‘complete’ and ‘incomplete’
markets? 155
37. Can I use real probabilities to price derivatives? 160